Properties

Label 735.2.p.a.509.2
Level $735$
Weight $2$
Character 735.509
Analytic conductor $5.869$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,2,Mod(374,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.374");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 509.2
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 735.509
Dual form 735.2.p.a.374.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.09077 - 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} -1.73205 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.09077 - 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} -1.73205 q^{8} +(-1.94949 - 2.28024i) q^{9} +(-0.621320 + 3.82282i) q^{10} +(2.44949 - 1.41421i) q^{11} +(-1.72474 + 0.158919i) q^{12} +4.00000 q^{13} +(0.267949 - 3.86370i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.44949 + 1.41421i) q^{17} +(5.10867 - 0.949490i) q^{18} +(-1.73205 - 1.41421i) q^{20} +4.89898i q^{22} +(-1.73205 + 3.00000i) q^{23} +(-1.25529 + 2.72474i) q^{24} +(3.74264 - 3.31552i) q^{25} +(-3.46410 + 6.00000i) q^{26} +(-5.00000 + 1.41421i) q^{27} -5.65685i q^{29} +(5.56350 + 3.74799i) q^{30} +(8.48528 - 4.89898i) q^{31} +(2.59808 + 4.50000i) q^{32} +(-0.449490 - 4.87832i) q^{33} -4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(2.89898 - 6.29253i) q^{39} +(-3.62132 + 1.37333i) q^{40} -3.46410 q^{41} -4.89898i q^{43} +(-2.44949 - 1.41421i) q^{44} +(-5.88392 - 3.22172i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(2.44949 + 1.41421i) q^{47} +(-5.00000 - 7.07107i) q^{48} +(1.73205 + 8.48528i) q^{50} +(0.449490 + 4.87832i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(2.20881 - 8.72474i) q^{54} +(4.00000 - 4.89898i) q^{55} +(8.48528 + 4.89898i) q^{58} +(-3.46410 - 6.00000i) q^{59} +(-3.48004 + 1.69980i) q^{60} +(8.48528 + 4.89898i) q^{61} +16.9706i q^{62} +1.00000 q^{64} +(8.36308 - 3.17157i) q^{65} +(7.70674 + 3.55051i) q^{66} +(4.24264 - 2.44949i) q^{67} +(2.44949 + 1.41421i) q^{68} +(3.46410 + 4.89898i) q^{69} +2.82843i q^{71} +(3.37662 + 3.94949i) q^{72} +(4.00000 + 6.92820i) q^{73} +(-2.50328 - 8.29057i) q^{75} +(6.92820 + 9.79796i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(1.79360 - 11.0355i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(3.00000 - 5.19615i) q^{82} -2.82843i q^{83} +(-4.00000 + 4.89898i) q^{85} +(7.34847 + 4.24264i) q^{86} +(-8.89898 - 4.09978i) q^{87} +(-4.24264 + 2.44949i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(9.92820 - 6.03579i) q^{90} +3.46410 q^{92} +(-1.55708 - 16.8990i) q^{93} +(-4.24264 + 2.44949i) q^{94} +(8.96204 - 0.825765i) q^{96} -8.00000 q^{97} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} - 4 q^{4} + 4 q^{9} + 12 q^{10} - 4 q^{12} + 32 q^{13} + 16 q^{15} + 20 q^{16} - 4 q^{25} - 40 q^{27} + 12 q^{30} + 16 q^{33} - 8 q^{36} - 16 q^{39} - 12 q^{40} - 16 q^{45} - 24 q^{46} - 40 q^{48} - 16 q^{51} - 16 q^{52} + 32 q^{55} - 8 q^{60} + 8 q^{64} + 32 q^{73} - 4 q^{75} - 32 q^{79} + 28 q^{81} + 24 q^{82} - 32 q^{85} - 32 q^{87} + 24 q^{90} - 64 q^{97} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 1.50000i −0.612372 + 1.06066i 0.378467 + 0.925615i \(0.376451\pi\)
−0.990839 + 0.135045i \(0.956882\pi\)
\(3\) 0.724745 1.57313i 0.418432 0.908248i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.09077 0.792893i 0.935021 0.354593i
\(6\) 1.73205 + 2.44949i 0.707107 + 1.00000i
\(7\) 0 0
\(8\) −1.73205 −0.612372
\(9\) −1.94949 2.28024i −0.649830 0.760080i
\(10\) −0.621320 + 3.82282i −0.196479 + 1.20888i
\(11\) 2.44949 1.41421i 0.738549 0.426401i −0.0829925 0.996550i \(-0.526448\pi\)
0.821541 + 0.570149i \(0.193114\pi\)
\(12\) −1.72474 + 0.158919i −0.497891 + 0.0458759i
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0.267949 3.86370i 0.0691842 0.997604i
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −2.44949 + 1.41421i −0.594089 + 0.342997i −0.766712 0.641991i \(-0.778109\pi\)
0.172624 + 0.984988i \(0.444775\pi\)
\(18\) 5.10867 0.949490i 1.20412 0.223797i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) −1.73205 1.41421i −0.387298 0.316228i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) −1.25529 + 2.72474i −0.256236 + 0.556186i
\(25\) 3.74264 3.31552i 0.748528 0.663103i
\(26\) −3.46410 + 6.00000i −0.679366 + 1.17670i
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) 0 0
\(29\) 5.65685i 1.05045i −0.850963 0.525226i \(-0.823981\pi\)
0.850963 0.525226i \(-0.176019\pi\)
\(30\) 5.56350 + 3.74799i 1.01575 + 0.684286i
\(31\) 8.48528 4.89898i 1.52400 0.879883i 0.524405 0.851469i \(-0.324288\pi\)
0.999596 0.0284139i \(-0.00904564\pi\)
\(32\) 2.59808 + 4.50000i 0.459279 + 0.795495i
\(33\) −0.449490 4.87832i −0.0782461 0.849206i
\(34\) 4.89898i 0.840168i
\(35\) 0 0
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 2.89898 6.29253i 0.464208 1.00761i
\(40\) −3.62132 + 1.37333i −0.572581 + 0.217143i
\(41\) −3.46410 −0.541002 −0.270501 0.962720i \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(42\) 0 0
\(43\) 4.89898i 0.747087i −0.927613 0.373544i \(-0.878143\pi\)
0.927613 0.373544i \(-0.121857\pi\)
\(44\) −2.44949 1.41421i −0.369274 0.213201i
\(45\) −5.88392 3.22172i −0.877123 0.480265i
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 2.44949 + 1.41421i 0.357295 + 0.206284i 0.667893 0.744257i \(-0.267196\pi\)
−0.310599 + 0.950541i \(0.600530\pi\)
\(48\) −5.00000 7.07107i −0.721688 1.02062i
\(49\) 0 0
\(50\) 1.73205 + 8.48528i 0.244949 + 1.20000i
\(51\) 0.449490 + 4.87832i 0.0629412 + 0.683101i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 2.20881 8.72474i 0.300581 1.18729i
\(55\) 4.00000 4.89898i 0.539360 0.660578i
\(56\) 0 0
\(57\) 0 0
\(58\) 8.48528 + 4.89898i 1.11417 + 0.643268i
\(59\) −3.46410 6.00000i −0.450988 0.781133i 0.547460 0.836832i \(-0.315595\pi\)
−0.998448 + 0.0556984i \(0.982261\pi\)
\(60\) −3.48004 + 1.69980i −0.449271 + 0.219443i
\(61\) 8.48528 + 4.89898i 1.08643 + 0.627250i 0.932623 0.360851i \(-0.117514\pi\)
0.153806 + 0.988101i \(0.450847\pi\)
\(62\) 16.9706i 2.15526i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.36308 3.17157i 1.03731 0.393385i
\(66\) 7.70674 + 3.55051i 0.948634 + 0.437038i
\(67\) 4.24264 2.44949i 0.518321 0.299253i −0.217926 0.975965i \(-0.569929\pi\)
0.736247 + 0.676712i \(0.236596\pi\)
\(68\) 2.44949 + 1.41421i 0.297044 + 0.171499i
\(69\) 3.46410 + 4.89898i 0.417029 + 0.589768i
\(70\) 0 0
\(71\) 2.82843i 0.335673i 0.985815 + 0.167836i \(0.0536780\pi\)
−0.985815 + 0.167836i \(0.946322\pi\)
\(72\) 3.37662 + 3.94949i 0.397938 + 0.465452i
\(73\) 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i \(-0.0115821\pi\)
−0.531174 + 0.847263i \(0.678249\pi\)
\(74\) 0 0
\(75\) −2.50328 8.29057i −0.289054 0.957313i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.92820 + 9.79796i 0.784465 + 1.10940i
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 1.79360 11.0355i 0.200530 1.23381i
\(81\) −1.39898 + 8.89060i −0.155442 + 0.987845i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) 0 0
\(85\) −4.00000 + 4.89898i −0.433861 + 0.531369i
\(86\) 7.34847 + 4.24264i 0.792406 + 0.457496i
\(87\) −8.89898 4.09978i −0.954071 0.439542i
\(88\) −4.24264 + 2.44949i −0.452267 + 0.261116i
\(89\) −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i \(0.352341\pi\)
−0.998218 + 0.0596775i \(0.980993\pi\)
\(90\) 9.92820 6.03579i 1.04652 0.636228i
\(91\) 0 0
\(92\) 3.46410 0.361158
\(93\) −1.55708 16.8990i −0.161461 1.75234i
\(94\) −4.24264 + 2.44949i −0.437595 + 0.252646i
\(95\) 0 0
\(96\) 8.96204 0.825765i 0.914684 0.0842793i
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) −8.00000 2.82843i −0.804030 0.284268i
\(100\) −4.74264 1.58346i −0.474264 0.158346i
\(101\) 8.66025 + 15.0000i 0.861727 + 1.49256i 0.870260 + 0.492592i \(0.163951\pi\)
−0.00853278 + 0.999964i \(0.502716\pi\)
\(102\) −7.70674 3.55051i −0.763081 0.351553i
\(103\) −5.00000 + 8.66025i −0.492665 + 0.853320i −0.999964 0.00844953i \(-0.997310\pi\)
0.507300 + 0.861770i \(0.330644\pi\)
\(104\) −6.92820 −0.679366
\(105\) 0 0
\(106\) 0 0
\(107\) 5.19615 9.00000i 0.502331 0.870063i −0.497665 0.867369i \(-0.665809\pi\)
0.999996 0.00269372i \(-0.000857438\pi\)
\(108\) 3.72474 + 3.62302i 0.358414 + 0.348625i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 3.88437 + 10.2426i 0.370360 + 0.976597i
\(111\) 0 0
\(112\) 0 0
\(113\) −6.92820 −0.651751 −0.325875 0.945413i \(-0.605659\pi\)
−0.325875 + 0.945413i \(0.605659\pi\)
\(114\) 0 0
\(115\) −1.24264 + 7.64564i −0.115877 + 0.712960i
\(116\) −4.89898 + 2.82843i −0.454859 + 0.262613i
\(117\) −7.79796 9.12096i −0.720922 0.843233i
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −0.464102 + 6.69213i −0.0423665 + 0.610905i
\(121\) −1.50000 + 2.59808i −0.136364 + 0.236189i
\(122\) −14.6969 + 8.48528i −1.33060 + 0.768221i
\(123\) −2.51059 + 5.44949i −0.226372 + 0.491364i
\(124\) −8.48528 4.89898i −0.762001 0.439941i
\(125\) 5.19615 9.89949i 0.464758 0.885438i
\(126\) 0 0
\(127\) 14.6969i 1.30414i −0.758158 0.652071i \(-0.773900\pi\)
0.758158 0.652071i \(-0.226100\pi\)
\(128\) −6.06218 + 10.5000i −0.535826 + 0.928078i
\(129\) −7.70674 3.55051i −0.678541 0.312605i
\(130\) −2.48528 + 15.2913i −0.217974 + 1.34113i
\(131\) −3.46410 + 6.00000i −0.302660 + 0.524222i −0.976738 0.214438i \(-0.931208\pi\)
0.674078 + 0.738661i \(0.264541\pi\)
\(132\) −4.00000 + 2.82843i −0.348155 + 0.246183i
\(133\) 0 0
\(134\) 8.48528i 0.733017i
\(135\) −9.33253 + 6.92126i −0.803216 + 0.595687i
\(136\) 4.24264 2.44949i 0.363803 0.210042i
\(137\) −3.46410 6.00000i −0.295958 0.512615i 0.679249 0.733908i \(-0.262306\pi\)
−0.975207 + 0.221293i \(0.928972\pi\)
\(138\) −10.3485 + 0.953512i −0.880920 + 0.0811683i
\(139\) 9.79796i 0.831052i 0.909581 + 0.415526i \(0.136402\pi\)
−0.909581 + 0.415526i \(0.863598\pi\)
\(140\) 0 0
\(141\) 4.00000 2.82843i 0.336861 0.238197i
\(142\) −4.24264 2.44949i −0.356034 0.205557i
\(143\) 9.79796 5.65685i 0.819346 0.473050i
\(144\) −14.7474 + 2.74094i −1.22895 + 0.228412i
\(145\) −4.48528 11.8272i −0.372482 0.982194i
\(146\) −13.8564 −1.14676
\(147\) 0 0
\(148\) 0 0
\(149\) −9.79796 5.65685i −0.802680 0.463428i 0.0417274 0.999129i \(-0.486714\pi\)
−0.844407 + 0.535701i \(0.820047\pi\)
\(150\) 14.6038 + 3.42492i 1.19239 + 0.279643i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 8.00000 + 2.82843i 0.646762 + 0.228665i
\(154\) 0 0
\(155\) 13.8564 16.9706i 1.11297 1.36311i
\(156\) −6.89898 + 0.635674i −0.552360 + 0.0508947i
\(157\) −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) −6.92820 12.0000i −0.551178 0.954669i
\(159\) 0 0
\(160\) 9.00000 + 7.34847i 0.711512 + 0.580948i
\(161\) 0 0
\(162\) −12.1244 9.79796i −0.952579 0.769800i
\(163\) −12.7279 7.34847i −0.996928 0.575577i −0.0895899 0.995979i \(-0.528556\pi\)
−0.907338 + 0.420402i \(0.861889\pi\)
\(164\) 1.73205 + 3.00000i 0.135250 + 0.234261i
\(165\) −4.80776 9.84304i −0.374284 0.766280i
\(166\) 4.24264 + 2.44949i 0.329293 + 0.190117i
\(167\) 14.1421i 1.09435i 0.837018 + 0.547176i \(0.184297\pi\)
−0.837018 + 0.547176i \(0.815703\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −3.88437 10.2426i −0.297917 0.785575i
\(171\) 0 0
\(172\) −4.24264 + 2.44949i −0.323498 + 0.186772i
\(173\) 17.1464 + 9.89949i 1.30362 + 0.752645i 0.981023 0.193892i \(-0.0621112\pi\)
0.322596 + 0.946537i \(0.395445\pi\)
\(174\) 13.8564 9.79796i 1.05045 0.742781i
\(175\) 0 0
\(176\) 14.1421i 1.06600i
\(177\) −11.9494 + 1.10102i −0.898171 + 0.0827578i
\(178\) −9.00000 15.5885i −0.674579 1.16840i
\(179\) 2.44949 1.41421i 0.183083 0.105703i −0.405657 0.914025i \(-0.632957\pi\)
0.588741 + 0.808322i \(0.299624\pi\)
\(180\) 0.151870 + 6.70648i 0.0113198 + 0.499872i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 13.8564 9.79796i 1.02430 0.724286i
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 0 0
\(186\) 26.6969 + 12.2993i 1.95751 + 0.901831i
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) 2.82843i 0.206284i
\(189\) 0 0
\(190\) 0 0
\(191\) −17.1464 9.89949i −1.24067 0.716302i −0.271441 0.962455i \(-0.587500\pi\)
−0.969231 + 0.246153i \(0.920834\pi\)
\(192\) 0.724745 1.57313i 0.0523040 0.113531i
\(193\) −8.48528 + 4.89898i −0.610784 + 0.352636i −0.773272 0.634074i \(-0.781381\pi\)
0.162488 + 0.986710i \(0.448048\pi\)
\(194\) 6.92820 12.0000i 0.497416 0.861550i
\(195\) 1.07180 15.4548i 0.0767530 1.10674i
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 11.1708 9.55051i 0.793877 0.678725i
\(199\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) −6.48244 + 5.74264i −0.458378 + 0.406066i
\(201\) −0.778539 8.44949i −0.0549139 0.595981i
\(202\) −30.0000 −2.11079
\(203\) 0 0
\(204\) 4.00000 2.82843i 0.280056 0.198030i
\(205\) −7.24264 + 2.74666i −0.505848 + 0.191835i
\(206\) −8.66025 15.0000i −0.603388 1.04510i
\(207\) 10.2173 1.89898i 0.710154 0.131988i
\(208\) 10.0000 17.3205i 0.693375 1.20096i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 4.44949 + 2.04989i 0.304874 + 0.140456i
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) −3.88437 10.2426i −0.264912 0.698542i
\(216\) 8.66025 2.44949i 0.589256 0.166667i
\(217\) 0 0
\(218\) −17.3205 −1.17309
\(219\) 13.7980 1.27135i 0.932380 0.0859098i
\(220\) −6.24264 1.01461i −0.420879 0.0684051i
\(221\) −9.79796 + 5.65685i −0.659082 + 0.380521i
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 0 0
\(225\) −14.8564 2.07055i −0.990427 0.138037i
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) −2.44949 + 1.41421i −0.162578 + 0.0938647i −0.579082 0.815270i \(-0.696589\pi\)
0.416503 + 0.909134i \(0.363255\pi\)
\(228\) 0 0
\(229\) 16.9706 + 9.79796i 1.12145 + 0.647467i 0.941770 0.336258i \(-0.109162\pi\)
0.179677 + 0.983726i \(0.442495\pi\)
\(230\) −10.3923 8.48528i −0.685248 0.559503i
\(231\) 0 0
\(232\) 9.79796i 0.643268i
\(233\) −10.3923 + 18.0000i −0.680823 + 1.17922i 0.293908 + 0.955834i \(0.405044\pi\)
−0.974730 + 0.223385i \(0.928289\pi\)
\(234\) 20.4347 3.79796i 1.33586 0.248280i
\(235\) 6.24264 + 1.01461i 0.407225 + 0.0661860i
\(236\) −3.46410 + 6.00000i −0.225494 + 0.390567i
\(237\) 8.00000 + 11.3137i 0.519656 + 0.734904i
\(238\) 0 0
\(239\) 2.82843i 0.182956i 0.995807 + 0.0914779i \(0.0291591\pi\)
−0.995807 + 0.0914779i \(0.970841\pi\)
\(240\) −16.0605 10.8195i −1.03670 0.698397i
\(241\) −8.48528 + 4.89898i −0.546585 + 0.315571i −0.747743 0.663988i \(-0.768863\pi\)
0.201158 + 0.979559i \(0.435529\pi\)
\(242\) −2.59808 4.50000i −0.167011 0.289271i
\(243\) 12.9722 + 8.64420i 0.832167 + 0.554526i
\(244\) 9.79796i 0.627250i
\(245\) 0 0
\(246\) −6.00000 8.48528i −0.382546 0.541002i
\(247\) 0 0
\(248\) −14.6969 + 8.48528i −0.933257 + 0.538816i
\(249\) −4.44949 2.04989i −0.281975 0.129906i
\(250\) 10.3492 + 16.3674i 0.654544 + 1.03517i
\(251\) 20.7846 1.31191 0.655956 0.754799i \(-0.272265\pi\)
0.655956 + 0.754799i \(0.272265\pi\)
\(252\) 0 0
\(253\) 9.79796i 0.615992i
\(254\) 22.0454 + 12.7279i 1.38325 + 0.798621i
\(255\) 4.80776 + 9.84304i 0.301074 + 0.616395i
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −12.2474 7.07107i −0.763975 0.441081i 0.0667462 0.997770i \(-0.478738\pi\)
−0.830721 + 0.556689i \(0.812072\pi\)
\(258\) 12.0000 8.48528i 0.747087 0.528271i
\(259\) 0 0
\(260\) −6.92820 5.65685i −0.429669 0.350823i
\(261\) −12.8990 + 11.0280i −0.798427 + 0.682615i
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) 1.73205 + 3.00000i 0.106803 + 0.184988i 0.914473 0.404646i \(-0.132605\pi\)
−0.807671 + 0.589634i \(0.799272\pi\)
\(264\) 0.778539 + 8.44949i 0.0479158 + 0.520030i
\(265\) 0 0
\(266\) 0 0
\(267\) 10.3923 + 14.6969i 0.635999 + 0.899438i
\(268\) −4.24264 2.44949i −0.259161 0.149626i
\(269\) 5.19615 + 9.00000i 0.316815 + 0.548740i 0.979822 0.199874i \(-0.0640532\pi\)
−0.663007 + 0.748614i \(0.730720\pi\)
\(270\) −2.29968 19.9928i −0.139954 1.21672i
\(271\) −25.4558 14.6969i −1.54633 0.892775i −0.998417 0.0562416i \(-0.982088\pi\)
−0.547915 0.836534i \(-0.684578\pi\)
\(272\) 14.1421i 0.857493i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 4.47871 13.4142i 0.270077 0.808908i
\(276\) 2.51059 5.44949i 0.151120 0.328021i
\(277\) −16.9706 + 9.79796i −1.01966 + 0.588702i −0.914006 0.405700i \(-0.867028\pi\)
−0.105656 + 0.994403i \(0.533694\pi\)
\(278\) −14.6969 8.48528i −0.881464 0.508913i
\(279\) −27.7128 9.79796i −1.65912 0.586588i
\(280\) 0 0
\(281\) 28.2843i 1.68730i 0.536895 + 0.843649i \(0.319597\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0.778539 + 8.44949i 0.0463613 + 0.503160i
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 2.44949 1.41421i 0.145350 0.0839181i
\(285\) 0 0
\(286\) 19.5959i 1.15873i
\(287\) 0 0
\(288\) 5.19615 14.6969i 0.306186 0.866025i
\(289\) −4.50000 + 7.79423i −0.264706 + 0.458484i
\(290\) 21.6251 + 3.51472i 1.26987 + 0.206391i
\(291\) −5.79796 + 12.5851i −0.339882 + 0.737749i
\(292\) 4.00000 6.92820i 0.234082 0.405442i
\(293\) 2.82843i 0.165238i −0.996581 0.0826192i \(-0.973671\pi\)
0.996581 0.0826192i \(-0.0263285\pi\)
\(294\) 0 0
\(295\) −12.0000 9.79796i −0.698667 0.570459i
\(296\) 0 0
\(297\) −10.2474 + 10.5352i −0.594617 + 0.611313i
\(298\) 16.9706 9.79796i 0.983078 0.567581i
\(299\) −6.92820 + 12.0000i −0.400668 + 0.693978i
\(300\) −5.92820 + 6.31319i −0.342265 + 0.364492i
\(301\) 0 0
\(302\) 13.8564 0.797347
\(303\) 29.8735 2.75255i 1.71619 0.158130i
\(304\) 0 0
\(305\) 21.6251 + 3.51472i 1.23825 + 0.201252i
\(306\) −11.1708 + 9.55051i −0.638595 + 0.545966i
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 10.0000 + 14.1421i 0.568880 + 0.804518i
\(310\) 13.4558 + 35.4815i 0.764241 + 2.01522i
\(311\) −13.8564 24.0000i −0.785725 1.36092i −0.928565 0.371169i \(-0.878957\pi\)
0.142840 0.989746i \(-0.454376\pi\)
\(312\) −5.02118 + 10.8990i −0.284268 + 0.617033i
\(313\) −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i \(-0.982689\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(314\) 6.92820 0.390981
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 6.92820 12.0000i 0.389127 0.673987i −0.603206 0.797586i \(-0.706110\pi\)
0.992332 + 0.123599i \(0.0394435\pi\)
\(318\) 0 0
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) 2.09077 0.792893i 0.116878 0.0443241i
\(321\) −10.3923 14.6969i −0.580042 0.820303i
\(322\) 0 0
\(323\) 0 0
\(324\) 8.39898 3.23375i 0.466610 0.179653i
\(325\) 14.9706 13.2621i 0.830417 0.735647i
\(326\) 22.0454 12.7279i 1.22098 0.704934i
\(327\) 17.2474 1.58919i 0.953786 0.0878822i
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 18.9282 + 1.31268i 1.04196 + 0.0722605i
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) −2.44949 + 1.41421i −0.134433 + 0.0776151i
\(333\) 0 0
\(334\) −21.2132 12.2474i −1.16073 0.670151i
\(335\) 6.92820 8.48528i 0.378528 0.463600i
\(336\) 0 0
\(337\) 19.5959i 1.06746i 0.845656 + 0.533729i \(0.179210\pi\)
−0.845656 + 0.533729i \(0.820790\pi\)
\(338\) −2.59808 + 4.50000i −0.141317 + 0.244768i
\(339\) −5.02118 + 10.8990i −0.272713 + 0.591951i
\(340\) 6.24264 + 1.01461i 0.338555 + 0.0550251i
\(341\) 13.8564 24.0000i 0.750366 1.29967i
\(342\) 0 0
\(343\) 0 0
\(344\) 8.48528i 0.457496i
\(345\) 11.1270 + 7.49598i 0.599058 + 0.403570i
\(346\) −29.6985 + 17.1464i −1.59660 + 0.921798i
\(347\) 8.66025 + 15.0000i 0.464907 + 0.805242i 0.999197 0.0400587i \(-0.0127545\pi\)
−0.534291 + 0.845301i \(0.679421\pi\)
\(348\) 0.898979 + 9.75663i 0.0481904 + 0.523010i
\(349\) 19.5959i 1.04895i 0.851427 + 0.524473i \(0.175738\pi\)
−0.851427 + 0.524473i \(0.824262\pi\)
\(350\) 0 0
\(351\) −20.0000 + 5.65685i −1.06752 + 0.301941i
\(352\) 12.7279 + 7.34847i 0.678401 + 0.391675i
\(353\) 26.9444 15.5563i 1.43411 0.827981i 0.436674 0.899620i \(-0.356156\pi\)
0.997431 + 0.0716387i \(0.0228229\pi\)
\(354\) 8.69694 18.8776i 0.462237 1.00333i
\(355\) 2.24264 + 5.91359i 0.119027 + 0.313861i
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) 4.89898i 0.258919i
\(359\) 26.9444 + 15.5563i 1.42207 + 0.821033i 0.996476 0.0838812i \(-0.0267316\pi\)
0.425595 + 0.904914i \(0.360065\pi\)
\(360\) 10.1913 + 5.58018i 0.537126 + 0.294101i
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) 0 0
\(363\) 3.00000 + 4.24264i 0.157459 + 0.222681i
\(364\) 0 0
\(365\) 13.8564 + 11.3137i 0.725277 + 0.592187i
\(366\) 2.69694 + 29.2699i 0.140971 + 1.52996i
\(367\) −5.00000 8.66025i −0.260998 0.452062i 0.705509 0.708700i \(-0.250718\pi\)
−0.966507 + 0.256639i \(0.917385\pi\)
\(368\) 8.66025 + 15.0000i 0.451447 + 0.781929i
\(369\) 6.75323 + 7.89898i 0.351559 + 0.411204i
\(370\) 0 0
\(371\) 0 0
\(372\) −13.8564 + 9.79796i −0.718421 + 0.508001i
\(373\) 8.48528 + 4.89898i 0.439351 + 0.253660i 0.703322 0.710871i \(-0.251699\pi\)
−0.263971 + 0.964531i \(0.585032\pi\)
\(374\) −6.92820 12.0000i −0.358249 0.620505i
\(375\) −11.8073 15.3488i −0.609728 0.792611i
\(376\) −4.24264 2.44949i −0.218797 0.126323i
\(377\) 22.6274i 1.16537i
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −23.1202 10.6515i −1.18449 0.545694i
\(382\) 29.6985 17.1464i 1.51951 0.877288i
\(383\) −12.2474 7.07107i −0.625815 0.361315i 0.153314 0.988177i \(-0.451005\pi\)
−0.779130 + 0.626863i \(0.784339\pi\)
\(384\) 12.1244 + 17.1464i 0.618718 + 0.875000i
\(385\) 0 0
\(386\) 16.9706i 0.863779i
\(387\) −11.1708 + 9.55051i −0.567846 + 0.485480i
\(388\) 4.00000 + 6.92820i 0.203069 + 0.351726i
\(389\) −19.5959 + 11.3137i −0.993552 + 0.573628i −0.906334 0.422561i \(-0.861131\pi\)
−0.0872182 + 0.996189i \(0.527798\pi\)
\(390\) 22.2540 + 14.9920i 1.12688 + 0.759147i
\(391\) 9.79796i 0.495504i
\(392\) 0 0
\(393\) 6.92820 + 9.79796i 0.349482 + 0.494242i
\(394\) 0 0
\(395\) −2.86976 + 17.6569i −0.144393 + 0.888413i
\(396\) 1.55051 + 8.34242i 0.0779161 + 0.419222i
\(397\) 10.0000 17.3205i 0.501886 0.869291i −0.498112 0.867113i \(-0.665973\pi\)
0.999998 0.00217869i \(-0.000693499\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −5.00000 24.4949i −0.250000 1.22474i
\(401\) 19.5959 + 11.3137i 0.978573 + 0.564980i 0.901839 0.432072i \(-0.142217\pi\)
0.0767343 + 0.997052i \(0.475551\pi\)
\(402\) 13.3485 + 6.14966i 0.665761 + 0.306717i
\(403\) 33.9411 19.5959i 1.69073 0.976142i
\(404\) 8.66025 15.0000i 0.430864 0.746278i
\(405\) 4.12436 + 19.6975i 0.204941 + 0.978774i
\(406\) 0 0
\(407\) 0 0
\(408\) −0.778539 8.44949i −0.0385434 0.418312i
\(409\) 8.48528 4.89898i 0.419570 0.242239i −0.275323 0.961352i \(-0.588785\pi\)
0.694893 + 0.719113i \(0.255452\pi\)
\(410\) 2.15232 13.2426i 0.106295 0.654007i
\(411\) −11.9494 + 1.10102i −0.589420 + 0.0543093i
\(412\) 10.0000 0.492665
\(413\) 0 0
\(414\) −6.00000 + 16.9706i −0.294884 + 0.834058i
\(415\) −2.24264 5.91359i −0.110087 0.290287i
\(416\) 10.3923 + 18.0000i 0.509525 + 0.882523i
\(417\) 15.4135 + 7.10102i 0.754802 + 0.347738i
\(418\) 0 0
\(419\) 6.92820 0.338465 0.169232 0.985576i \(-0.445871\pi\)
0.169232 + 0.985576i \(0.445871\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 3.46410 6.00000i 0.168630 0.292075i
\(423\) −1.55051 8.34242i −0.0753884 0.405622i
\(424\) 0 0
\(425\) −4.47871 + 13.4142i −0.217250 + 0.650685i
\(426\) −6.92820 + 4.89898i −0.335673 + 0.237356i
\(427\) 0 0
\(428\) −10.3923 −0.502331
\(429\) −1.79796 19.5133i −0.0868063 0.942109i
\(430\) 18.7279 + 3.04384i 0.903141 + 0.146787i
\(431\) 2.44949 1.41421i 0.117988 0.0681203i −0.439845 0.898074i \(-0.644967\pi\)
0.557832 + 0.829954i \(0.311633\pi\)
\(432\) −6.37628 + 25.1862i −0.306779 + 1.21177i
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) −21.8564 1.51575i −1.04793 0.0726746i
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 0 0
\(438\) −10.0424 + 21.7980i −0.479842 + 1.04155i
\(439\) 33.9411 + 19.5959i 1.61992 + 0.935262i 0.986939 + 0.161096i \(0.0515030\pi\)
0.632983 + 0.774166i \(0.281830\pi\)
\(440\) −6.92820 + 8.48528i −0.330289 + 0.404520i
\(441\) 0 0
\(442\) 19.5959i 0.932083i
\(443\) −8.66025 + 15.0000i −0.411461 + 0.712672i −0.995050 0.0993779i \(-0.968315\pi\)
0.583589 + 0.812049i \(0.301648\pi\)
\(444\) 0 0
\(445\) −3.72792 + 22.9369i −0.176720 + 1.08731i
\(446\) 22.5167 39.0000i 1.06619 1.84670i
\(447\) −16.0000 + 11.3137i −0.756774 + 0.535120i
\(448\) 0 0
\(449\) 5.65685i 0.266963i −0.991051 0.133482i \(-0.957384\pi\)
0.991051 0.133482i \(-0.0426157\pi\)
\(450\) 15.9719 20.4915i 0.752920 0.965977i
\(451\) −8.48528 + 4.89898i −0.399556 + 0.230684i
\(452\) 3.46410 + 6.00000i 0.162938 + 0.282216i
\(453\) −13.7980 + 1.27135i −0.648285 + 0.0597332i
\(454\) 4.89898i 0.229920i
\(455\) 0 0
\(456\) 0 0
\(457\) 16.9706 + 9.79796i 0.793849 + 0.458329i 0.841316 0.540544i \(-0.181781\pi\)
−0.0474665 + 0.998873i \(0.515115\pi\)
\(458\) −29.3939 + 16.9706i −1.37349 + 0.792982i
\(459\) 10.2474 10.5352i 0.478310 0.491740i
\(460\) 7.24264 2.74666i 0.337690 0.128064i
\(461\) 3.46410 0.161339 0.0806696 0.996741i \(-0.474294\pi\)
0.0806696 + 0.996741i \(0.474294\pi\)
\(462\) 0 0
\(463\) 4.89898i 0.227675i 0.993499 + 0.113837i \(0.0363143\pi\)
−0.993499 + 0.113837i \(0.963686\pi\)
\(464\) −24.4949 14.1421i −1.13715 0.656532i
\(465\) −16.6546 34.0973i −0.772338 1.58122i
\(466\) −18.0000 31.1769i −0.833834 1.44424i
\(467\) 2.44949 + 1.41421i 0.113349 + 0.0654420i 0.555603 0.831448i \(-0.312488\pi\)
−0.442254 + 0.896890i \(0.645821\pi\)
\(468\) −4.00000 + 11.3137i −0.184900 + 0.522976i
\(469\) 0 0
\(470\) −6.92820 + 8.48528i −0.319574 + 0.391397i
\(471\) −6.89898 + 0.635674i −0.317888 + 0.0292903i
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) −6.92820 12.0000i −0.318559 0.551761i
\(474\) −23.8988 + 2.20204i −1.09771 + 0.101143i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −4.24264 2.44949i −0.194054 0.112037i
\(479\) 13.8564 + 24.0000i 0.633115 + 1.09659i 0.986911 + 0.161265i \(0.0515575\pi\)
−0.353796 + 0.935323i \(0.615109\pi\)
\(480\) 18.0828 8.83242i 0.825364 0.403143i
\(481\) 0 0
\(482\) 16.9706i 0.772988i
\(483\) 0 0
\(484\) 3.00000 0.136364
\(485\) −16.7262 + 6.34315i −0.759496 + 0.288027i
\(486\) −24.2005 + 11.9722i −1.09776 + 0.543070i
\(487\) −12.7279 + 7.34847i −0.576757 + 0.332991i −0.759844 0.650106i \(-0.774725\pi\)
0.183086 + 0.983097i \(0.441391\pi\)
\(488\) −14.6969 8.48528i −0.665299 0.384111i
\(489\) −20.7846 + 14.6969i −0.939913 + 0.664619i
\(490\) 0 0
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 5.97469 0.550510i 0.269360 0.0248189i
\(493\) 8.00000 + 13.8564i 0.360302 + 0.624061i
\(494\) 0 0
\(495\) −18.9688 + 0.429554i −0.852584 + 0.0193070i
\(496\) 48.9898i 2.19971i
\(497\) 0 0
\(498\) 6.92820 4.89898i 0.310460 0.219529i
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −11.1713 + 0.449747i −0.499595 + 0.0201133i
\(501\) 22.2474 + 10.2494i 0.993943 + 0.457911i
\(502\) −18.0000 + 31.1769i −0.803379 + 1.39149i
\(503\) 19.7990i 0.882793i −0.897312 0.441397i \(-0.854483\pi\)
0.897312 0.441397i \(-0.145517\pi\)
\(504\) 0 0
\(505\) 30.0000 + 24.4949i 1.33498 + 1.09001i
\(506\) −14.6969 8.48528i −0.653359 0.377217i
\(507\) 2.17423 4.71940i 0.0965611 0.209596i
\(508\) −12.7279 + 7.34847i −0.564710 + 0.326036i
\(509\) 1.73205 3.00000i 0.0767718 0.132973i −0.825084 0.565011i \(-0.808872\pi\)
0.901855 + 0.432038i \(0.142205\pi\)
\(510\) −18.9282 1.31268i −0.838155 0.0581263i
\(511\) 0 0
\(512\) 8.66025 0.382733
\(513\) 0 0
\(514\) 21.2132 12.2474i 0.935674 0.540212i
\(515\) −3.58719 + 22.0711i −0.158071 + 0.972567i
\(516\) 0.778539 + 8.44949i 0.0342733 + 0.371968i
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) 28.0000 19.7990i 1.22906 0.869079i
\(520\) −14.4853 + 5.49333i −0.635222 + 0.240898i
\(521\) 5.19615 + 9.00000i 0.227648 + 0.394297i 0.957110 0.289723i \(-0.0935633\pi\)
−0.729463 + 0.684020i \(0.760230\pi\)
\(522\) −5.37113 28.8990i −0.235088 1.26487i
\(523\) 13.0000 22.5167i 0.568450 0.984585i −0.428269 0.903651i \(-0.640876\pi\)
0.996719 0.0809336i \(-0.0257902\pi\)
\(524\) 6.92820 0.302660
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) −13.8564 + 24.0000i −0.603595 + 1.04546i
\(528\) −22.2474 10.2494i −0.968196 0.446050i
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 0 0
\(531\) −6.92820 + 19.5959i −0.300658 + 0.850390i
\(532\) 0 0
\(533\) −13.8564 −0.600188
\(534\) −31.0454 + 2.86054i −1.34347 + 0.123787i
\(535\) 3.72792 22.9369i 0.161172 0.991650i
\(536\) −7.34847 + 4.24264i −0.317406 + 0.183254i
\(537\) −0.449490 4.87832i −0.0193969 0.210515i
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) 10.6603 + 4.62158i 0.458744 + 0.198881i
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) 44.0908 25.4558i 1.89386 1.09342i
\(543\) 0 0
\(544\) −12.7279 7.34847i −0.545705 0.315063i
\(545\) 17.3205 + 14.1421i 0.741929 + 0.605783i
\(546\) 0 0
\(547\) 34.2929i 1.46626i −0.680090 0.733128i \(-0.738059\pi\)
0.680090 0.733128i \(-0.261941\pi\)
\(548\) −3.46410 + 6.00000i −0.147979 + 0.256307i
\(549\) −5.37113 28.8990i −0.229234 1.23338i
\(550\) 16.2426 + 18.3351i 0.692589 + 0.781812i
\(551\) 0 0
\(552\) −6.00000 8.48528i −0.255377 0.361158i
\(553\) 0 0
\(554\) 33.9411i 1.44202i
\(555\) 0 0
\(556\) 8.48528 4.89898i 0.359856 0.207763i
\(557\) −20.7846 36.0000i −0.880672 1.52537i −0.850595 0.525821i \(-0.823758\pi\)
−0.0300772 0.999548i \(-0.509575\pi\)
\(558\) 38.6969 33.0839i 1.63817 1.40055i
\(559\) 19.5959i 0.828819i
\(560\) 0 0
\(561\) 8.00000 + 11.3137i 0.337760 + 0.477665i
\(562\) −42.4264 24.4949i −1.78965 1.03325i
\(563\) 12.2474 7.07107i 0.516168 0.298010i −0.219197 0.975681i \(-0.570344\pi\)
0.735366 + 0.677671i \(0.237010\pi\)
\(564\) −4.44949 2.04989i −0.187357 0.0863159i
\(565\) −14.4853 + 5.49333i −0.609400 + 0.231106i
\(566\) −24.2487 −1.01925
\(567\) 0 0
\(568\) 4.89898i 0.205557i
\(569\) −24.4949 14.1421i −1.02688 0.592869i −0.110790 0.993844i \(-0.535338\pi\)
−0.916089 + 0.400975i \(0.868672\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) −9.79796 5.65685i −0.409673 0.236525i
\(573\) −28.0000 + 19.7990i −1.16972 + 0.827115i
\(574\) 0 0
\(575\) 3.46410 + 16.9706i 0.144463 + 0.707721i
\(576\) −1.94949 2.28024i −0.0812287 0.0950100i
\(577\) 4.00000 + 6.92820i 0.166522 + 0.288425i 0.937195 0.348806i \(-0.113413\pi\)
−0.770673 + 0.637231i \(0.780080\pi\)
\(578\) −7.79423 13.5000i −0.324197 0.561526i
\(579\) 1.55708 + 16.8990i 0.0647100 + 0.702298i
\(580\) −8.00000 + 9.79796i −0.332182 + 0.406838i
\(581\) 0 0
\(582\) −13.8564 19.5959i −0.574367 0.812277i
\(583\) 0 0
\(584\) −6.92820 12.0000i −0.286691 0.496564i
\(585\) −23.5357 12.8869i −0.973081 0.532807i
\(586\) 4.24264 + 2.44949i 0.175262 + 0.101187i
\(587\) 19.7990i 0.817192i −0.912715 0.408596i \(-0.866019\pi\)
0.912715 0.408596i \(-0.133981\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 25.0892 9.51472i 1.03291 0.391715i
\(591\) 0 0
\(592\) 0 0
\(593\) 17.1464 + 9.89949i 0.704119 + 0.406524i 0.808880 0.587974i \(-0.200074\pi\)
−0.104760 + 0.994497i \(0.533408\pi\)
\(594\) −6.92820 24.4949i −0.284268 1.00504i
\(595\) 0 0
\(596\) 11.3137i 0.463428i
\(597\) 0 0
\(598\) −12.0000 20.7846i −0.490716 0.849946i
\(599\) 31.8434 18.3848i 1.30108 0.751182i 0.320495 0.947250i \(-0.396151\pi\)
0.980590 + 0.196069i \(0.0628176\pi\)
\(600\) 4.33581 + 14.3597i 0.177009 + 0.586232i
\(601\) 9.79796i 0.399667i −0.979830 0.199834i \(-0.935960\pi\)
0.979830 0.199834i \(-0.0640401\pi\)
\(602\) 0 0
\(603\) −13.8564 4.89898i −0.564276 0.199502i
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −1.07616 + 6.62132i −0.0437521 + 0.269195i
\(606\) −21.7423 + 47.1940i −0.883222 + 1.91712i
\(607\) −5.00000 + 8.66025i −0.202944 + 0.351509i −0.949476 0.313841i \(-0.898384\pi\)
0.746532 + 0.665350i \(0.231718\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −24.0000 + 29.3939i −0.971732 + 1.19012i
\(611\) 9.79796 + 5.65685i 0.396383 + 0.228852i
\(612\) −1.55051 8.34242i −0.0626757 0.337222i
\(613\) −25.4558 + 14.6969i −1.02815 + 0.593604i −0.916455 0.400139i \(-0.868962\pi\)
−0.111697 + 0.993742i \(0.535629\pi\)
\(614\) −8.66025 + 15.0000i −0.349499 + 0.605351i
\(615\) −0.928203 + 13.3843i −0.0374288 + 0.539705i
\(616\) 0 0
\(617\) −48.4974 −1.95243 −0.976216 0.216799i \(-0.930439\pi\)
−0.976216 + 0.216799i \(0.930439\pi\)
\(618\) −29.8735 + 2.75255i −1.20169 + 0.110724i
\(619\) −8.48528 + 4.89898i −0.341052 + 0.196907i −0.660737 0.750617i \(-0.729756\pi\)
0.319685 + 0.947524i \(0.396423\pi\)
\(620\) −21.6251 3.51472i −0.868487 0.141154i
\(621\) 4.41761 17.4495i 0.177273 0.700224i
\(622\) 48.0000 1.92462
\(623\) 0 0
\(624\) −20.0000 28.2843i −0.800641 1.13228i
\(625\) 3.01472 24.8176i 0.120589 0.992703i
\(626\) −13.8564 24.0000i −0.553813 0.959233i
\(627\) 0 0
\(628\) −2.00000 + 3.46410i −0.0798087 + 0.138233i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 6.92820 12.0000i 0.275589 0.477334i
\(633\) −2.89898 + 6.29253i −0.115224 + 0.250106i
\(634\) 12.0000 + 20.7846i 0.476581 + 0.825462i
\(635\) −11.6531 30.7279i −0.462439 1.21940i
\(636\) 0 0
\(637\) 0 0
\(638\) 27.7128 1.09716
\(639\) 6.44949 5.51399i 0.255138 0.218130i
\(640\) −4.34924 + 26.7597i −0.171919 + 1.05777i
\(641\) −4.89898 + 2.82843i −0.193498 + 0.111716i −0.593619 0.804746i \(-0.702301\pi\)
0.400121 + 0.916462i \(0.368968\pi\)
\(642\) 31.0454 2.86054i 1.22526 0.112896i
\(643\) 22.0000 0.867595 0.433798 0.901010i \(-0.357173\pi\)
0.433798 + 0.901010i \(0.357173\pi\)
\(644\) 0 0
\(645\) −18.9282 1.31268i −0.745297 0.0516866i
\(646\) 0 0
\(647\) −17.1464 + 9.89949i −0.674096 + 0.389189i −0.797627 0.603151i \(-0.793911\pi\)
0.123531 + 0.992341i \(0.460578\pi\)
\(648\) 2.42310 15.3990i 0.0951885 0.604929i
\(649\) −16.9706 9.79796i −0.666153 0.384604i
\(650\) 6.92820 + 33.9411i 0.271746 + 1.33128i
\(651\) 0 0
\(652\) 14.6969i 0.575577i
\(653\) 13.8564 24.0000i 0.542243 0.939193i −0.456532 0.889707i \(-0.650909\pi\)
0.998775 0.0494855i \(-0.0157581\pi\)
\(654\) −12.5529 + 27.2474i −0.490859 + 1.06546i
\(655\) −2.48528 + 15.2913i −0.0971080 + 0.597480i
\(656\) −8.66025 + 15.0000i −0.338126 + 0.585652i
\(657\) 8.00000 22.6274i 0.312110 0.882780i
\(658\) 0 0
\(659\) 2.82843i 0.110180i 0.998481 + 0.0550899i \(0.0175446\pi\)
−0.998481 + 0.0550899i \(0.982455\pi\)
\(660\) −6.12044 + 9.08516i −0.238238 + 0.353640i
\(661\) 8.48528 4.89898i 0.330039 0.190548i −0.325819 0.945432i \(-0.605640\pi\)
0.655859 + 0.754884i \(0.272307\pi\)
\(662\) 24.2487 + 42.0000i 0.942453 + 1.63238i
\(663\) 1.79796 + 19.5133i 0.0698269 + 0.757832i
\(664\) 4.89898i 0.190117i
\(665\) 0 0
\(666\) 0 0
\(667\) 16.9706 + 9.79796i 0.657103 + 0.379378i
\(668\) 12.2474 7.07107i 0.473868 0.273588i
\(669\) −18.8434 + 40.9014i −0.728527 + 1.58134i
\(670\) 6.72792 + 17.7408i 0.259922 + 0.685386i
\(671\) 27.7128 1.06984
\(672\) 0 0
\(673\) 9.79796i 0.377684i 0.982008 + 0.188842i \(0.0604733\pi\)
−0.982008 + 0.188842i \(0.939527\pi\)
\(674\) −29.3939 16.9706i −1.13221 0.653682i
\(675\) −14.0244 + 21.8705i −0.539798 + 0.841795i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 2.44949 + 1.41421i 0.0941415 + 0.0543526i 0.546332 0.837569i \(-0.316024\pi\)
−0.452190 + 0.891922i \(0.649357\pi\)
\(678\) −12.0000 16.9706i −0.460857 0.651751i
\(679\) 0 0
\(680\) 6.92820 8.48528i 0.265684 0.325396i
\(681\) 0.449490 + 4.87832i 0.0172245 + 0.186937i
\(682\) 24.0000 + 41.5692i 0.919007 + 1.59177i
\(683\) 5.19615 + 9.00000i 0.198825 + 0.344375i 0.948148 0.317830i \(-0.102954\pi\)
−0.749323 + 0.662205i \(0.769621\pi\)
\(684\) 0 0
\(685\) −12.0000 9.79796i −0.458496 0.374361i
\(686\) 0 0
\(687\) 27.7128 19.5959i 1.05731 0.747631i
\(688\) −21.2132 12.2474i −0.808746 0.466930i
\(689\) 0 0
\(690\) −20.8802 + 10.1988i −0.794897 + 0.388262i
\(691\) 8.48528 + 4.89898i 0.322795 + 0.186366i 0.652638 0.757670i \(-0.273662\pi\)
−0.329843 + 0.944036i \(0.606996\pi\)
\(692\) 19.7990i 0.752645i
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 7.76874 + 20.4853i 0.294685 + 0.777051i
\(696\) 15.4135 + 7.10102i 0.584247 + 0.269163i
\(697\) 8.48528 4.89898i 0.321403 0.185562i
\(698\) −29.3939 16.9706i −1.11257 0.642345i
\(699\) 20.7846 + 29.3939i 0.786146 + 1.11178i
\(700\) 0 0
\(701\) 22.6274i 0.854626i −0.904104 0.427313i \(-0.859460\pi\)
0.904104 0.427313i \(-0.140540\pi\)
\(702\) 8.83523 34.8990i 0.333464 1.31718i
\(703\) 0 0
\(704\) 2.44949 1.41421i 0.0923186 0.0533002i
\(705\) 6.12044 9.08516i 0.230509 0.342167i
\(706\) 53.8888i 2.02813i
\(707\) 0 0
\(708\) 6.92820 + 9.79796i 0.260378 + 0.368230i
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) −10.8126 1.75736i −0.405789 0.0659525i
\(711\) 23.5959 4.38551i 0.884916 0.164469i
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 33.9411i 1.27111i
\(714\) 0 0
\(715\) 16.0000 19.5959i 0.598366 0.732846i
\(716\) −2.44949 1.41421i −0.0915417 0.0528516i
\(717\) 4.44949 + 2.04989i 0.166169 + 0.0765545i
\(718\) −46.6690 + 26.9444i −1.74167 + 1.00556i
\(719\) 20.7846 36.0000i 0.775135 1.34257i −0.159583 0.987184i \(-0.551015\pi\)
0.934718 0.355389i \(-0.115652\pi\)
\(720\) −28.6603 + 17.4238i −1.06810 + 0.649348i
\(721\) 0 0
\(722\) 32.9090 1.22474
\(723\) 1.55708 + 16.8990i 0.0579084 + 0.628480i
\(724\) 0 0
\(725\) −18.7554 21.1716i −0.696558 0.786292i
\(726\) −8.96204 + 0.825765i −0.332612 + 0.0306470i
\(727\) 10.0000 0.370879 0.185440 0.982656i \(-0.440629\pi\)
0.185440 + 0.982656i \(0.440629\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) −28.9706 + 10.9867i −1.07225 + 0.406634i
\(731\) 6.92820 + 12.0000i 0.256249 + 0.443836i
\(732\) −15.4135 7.10102i −0.569699 0.262461i
\(733\) −14.0000 + 24.2487i −0.517102 + 0.895647i 0.482701 + 0.875785i \(0.339656\pi\)
−0.999803 + 0.0198613i \(0.993678\pi\)
\(734\) 17.3205 0.639312
\(735\) 0 0
\(736\) −18.0000 −0.663489
\(737\) 6.92820 12.0000i 0.255204 0.442026i
\(738\) −17.6969 + 3.28913i −0.651433 + 0.121075i
\(739\) −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.2487 0.889599 0.444799 0.895630i \(-0.353275\pi\)
0.444799 + 0.895630i \(0.353275\pi\)
\(744\) 2.69694 + 29.2699i 0.0988746 + 1.07309i
\(745\) −24.9706 4.05845i −0.914851 0.148690i
\(746\) −14.6969 + 8.48528i −0.538093 + 0.310668i
\(747\) −6.44949 + 5.51399i −0.235974 + 0.201746i
\(748\) 8.00000 0.292509
\(749\) 0 0
\(750\) 33.2487 4.41851i 1.21407 0.161341i
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 12.2474 7.07107i 0.446619 0.257855i
\(753\) 15.0635 32.6969i 0.548946 1.19154i
\(754\) 33.9411 + 19.5959i 1.23606 + 0.713641i
\(755\) −13.8564 11.3137i −0.504286 0.411748i
\(756\) 0 0
\(757\) 29.3939i 1.06834i 0.845378 + 0.534169i \(0.179376\pi\)
−0.845378 + 0.534169i \(0.820624\pi\)
\(758\) 24.2487 42.0000i 0.880753 1.52551i
\(759\) 15.4135 + 7.10102i 0.559474 + 0.257751i
\(760\) 0 0
\(761\) −19.0526 + 33.0000i −0.690655 + 1.19625i 0.280969 + 0.959717i \(0.409344\pi\)
−0.971624 + 0.236532i \(0.923989\pi\)
\(762\) 36.0000 25.4558i 1.30414 0.922168i
\(763\) 0 0
\(764\) 19.7990i 0.716302i
\(765\) 18.9688 0.429554i 0.685819 0.0155306i
\(766\) 21.2132 12.2474i 0.766464 0.442518i
\(767\) −13.8564 24.0000i −0.500326 0.866590i
\(768\) −32.7702 + 3.01945i −1.18249 + 0.108955i
\(769\) 19.5959i 0.706647i −0.935501 0.353323i \(-0.885052\pi\)
0.935501 0.353323i \(-0.114948\pi\)
\(770\) 0 0
\(771\) −20.0000 + 14.1421i −0.720282 + 0.509317i
\(772\) 8.48528 + 4.89898i 0.305392 + 0.176318i
\(773\) −2.44949 + 1.41421i −0.0881020 + 0.0508657i −0.543404 0.839471i \(-0.682865\pi\)
0.455302 + 0.890337i \(0.349531\pi\)
\(774\) −4.65153 25.0273i −0.167196 0.899586i
\(775\) 15.5147 46.4682i 0.557305 1.66919i
\(776\) 13.8564 0.497416
\(777\) 0 0
\(778\) 39.1918i 1.40510i
\(779\) 0 0
\(780\) −13.9202 + 6.79920i −0.498422 + 0.243451i
\(781\) 4.00000 + 6.92820i 0.143131 + 0.247911i
\(782\) 14.6969 + 8.48528i 0.525561 + 0.303433i
\(783\) 8.00000 + 28.2843i 0.285897 + 1.01080i
\(784\) 0 0
\(785\) −6.92820 5.65685i −0.247278 0.201902i
\(786\) −20.6969 + 1.90702i −0.738235 + 0.0680213i
\(787\) 7.00000 + 12.1244i 0.249523 + 0.432187i 0.963394 0.268091i \(-0.0863928\pi\)
−0.713871 + 0.700278i \(0.753059\pi\)
\(788\) 0 0
\(789\) 5.97469 0.550510i 0.212705 0.0195987i
\(790\) −24.0000 19.5959i −0.853882 0.697191i
\(791\) 0 0
\(792\) 13.8564 + 4.89898i 0.492366 + 0.174078i
\(793\) 33.9411 + 19.5959i 1.20528 + 0.695871i
\(794\) 17.3205 + 30.0000i 0.614682 + 1.06466i
\(795\) 0 0
\(796\) 0 0
\(797\) 36.7696i 1.30244i −0.758887 0.651222i \(-0.774257\pi\)
0.758887 0.651222i \(-0.225743\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 24.6435 + 8.22792i 0.871279 + 0.290901i
\(801\) 30.6520 5.69694i 1.08304 0.201291i
\(802\) −33.9411 + 19.5959i −1.19850 + 0.691956i
\(803\) 19.5959 + 11.3137i 0.691525 + 0.399252i
\(804\) −6.92820 + 4.89898i −0.244339 + 0.172774i
\(805\) 0 0
\(806\) 67.8823i 2.39105i
\(807\) 17.9241 1.65153i 0.630957 0.0581366i
\(808\) −15.0000 25.9808i −0.527698 0.914000i
\(809\) −19.5959 + 11.3137i −0.688956 + 0.397769i −0.803221 0.595682i \(-0.796882\pi\)
0.114265 + 0.993450i \(0.463549\pi\)
\(810\) −33.1180 10.8720i −1.16365 0.382002i
\(811\) 29.3939i 1.03216i 0.856541 + 0.516079i \(0.172609\pi\)
−0.856541 + 0.516079i \(0.827391\pi\)
\(812\) 0 0
\(813\) −41.5692 + 29.3939i −1.45790 + 1.03089i
\(814\) 0 0
\(815\) −32.4377 5.27208i −1.13624 0.184673i
\(816\) 22.2474 + 10.2494i 0.778816 + 0.358802i
\(817\) 0 0
\(818\) 16.9706i 0.593362i
\(819\) 0 0
\(820\) 6.00000 + 4.89898i 0.209529 + 0.171080i
\(821\) 19.5959 + 11.3137i 0.683902 + 0.394851i 0.801324 0.598231i \(-0.204129\pi\)
−0.117421 + 0.993082i \(0.537463\pi\)
\(822\) 8.69694 18.8776i 0.303341 0.658431i
\(823\) 4.24264 2.44949i 0.147889 0.0853838i −0.424229 0.905555i \(-0.639455\pi\)
0.572119 + 0.820171i \(0.306122\pi\)
\(824\) 8.66025 15.0000i 0.301694 0.522550i
\(825\) −17.8564 16.7675i −0.621680 0.583769i
\(826\) 0 0
\(827\) −10.3923 −0.361376 −0.180688 0.983540i \(-0.557832\pi\)
−0.180688 + 0.983540i \(0.557832\pi\)
\(828\) −6.75323 7.89898i −0.234691 0.274509i
\(829\) −25.4558 + 14.6969i −0.884118 + 0.510446i −0.872014 0.489481i \(-0.837186\pi\)
−0.0121040 + 0.999927i \(0.503853\pi\)
\(830\) 10.8126 + 1.75736i 0.375310 + 0.0609988i
\(831\) 3.11416 + 33.7980i 0.108029 + 1.17244i
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) −24.0000 + 16.9706i −0.831052 + 0.587643i
\(835\) 11.2132 + 29.5680i 0.388049 + 1.02324i
\(836\) 0 0
\(837\) −35.4982 + 36.4949i −1.22700 + 1.26145i
\(838\) −6.00000 + 10.3923i −0.207267 + 0.358996i
\(839\) −27.7128 −0.956753 −0.478376 0.878155i \(-0.658774\pi\)
−0.478376 + 0.878155i \(0.658774\pi\)
\(840\) 0 0
\(841\) −3.00000 −0.103448
\(842\) −22.5167 + 39.0000i −0.775975 + 1.34403i
\(843\) 44.4949 + 20.4989i 1.53249 + 0.706019i
\(844\) 2.00000 + 3.46410i 0.0688428 + 0.119239i
\(845\) 6.27231 2.37868i 0.215774 0.0818291i
\(846\) 13.8564 + 4.89898i 0.476393 + 0.168430i
\(847\) 0 0
\(848\) 0 0
\(849\) 24.1464 2.22486i 0.828703 0.0763570i
\(850\) −16.2426 18.3351i −0.557118 0.628889i
\(851\) 0 0
\(852\) −0.449490 4.87832i −0.0153993 0.167128i
\(853\) −20.0000 −0.684787 −0.342393 0.939557i \(-0.611238\pi\)
−0.342393 + 0.939557i \(0.611238\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −9.00000 + 15.5885i −0.307614 + 0.532803i
\(857\) 41.6413 24.0416i 1.42244 0.821246i 0.425933 0.904754i \(-0.359946\pi\)
0.996507 + 0.0835080i \(0.0266124\pi\)
\(858\) 30.8270 + 14.2020i 1.05242 + 0.484850i
\(859\) −33.9411 19.5959i −1.15806 0.668604i −0.207219 0.978295i \(-0.566441\pi\)
−0.950837 + 0.309691i \(0.899775\pi\)
\(860\) −6.92820 + 8.48528i −0.236250 + 0.289346i
\(861\) 0 0
\(862\) 4.89898i 0.166860i
\(863\) 5.19615 9.00000i 0.176879 0.306364i −0.763931 0.645298i \(-0.776733\pi\)
0.940810 + 0.338935i \(0.110067\pi\)
\(864\) −19.3543 18.8258i −0.658448 0.640466i
\(865\) 43.6985 + 7.10228i 1.48579 + 0.241485i
\(866\) −13.8564 + 24.0000i −0.470860 + 0.815553i
\(867\) 9.00000 + 12.7279i 0.305656 + 0.432263i
\(868\) 0 0
\(869\) 22.6274i 0.767583i
\(870\) 21.2018 31.4719i 0.718809 1.06700i
\(871\) 16.9706 9.79796i 0.575026 0.331991i
\(872\) −8.66025 15.0000i −0.293273 0.507964i
\(873\) 15.5959 + 18.2419i 0.527842 + 0.617395i
\(874\) 0 0
\(875\) 0 0
\(876\) −8.00000 11.3137i −0.270295 0.382255i
\(877\) −42.4264 24.4949i −1.43264 0.827134i −0.435317 0.900277i \(-0.643364\pi\)
−0.997321 + 0.0731435i \(0.976697\pi\)
\(878\) −58.7878 + 33.9411i −1.98399 + 1.14546i
\(879\) −4.44949 2.04989i −0.150078 0.0691410i
\(880\) −11.2132 29.5680i −0.377997 0.996736i
\(881\) −10.3923 −0.350126 −0.175063 0.984557i \(-0.556013\pi\)
−0.175063 + 0.984557i \(0.556013\pi\)
\(882\) 0 0
\(883\) 14.6969i 0.494591i −0.968940 0.247296i \(-0.920458\pi\)
0.968940 0.247296i \(-0.0795419\pi\)
\(884\) 9.79796 + 5.65685i 0.329541 + 0.190261i
\(885\) −24.1104 + 11.7766i −0.810463 + 0.395865i
\(886\) −15.0000 25.9808i −0.503935 0.872841i
\(887\) 2.44949 + 1.41421i 0.0822458 + 0.0474846i 0.540559 0.841306i \(-0.318213\pi\)
−0.458313 + 0.888791i \(0.651546\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −31.1769 25.4558i −1.04505 0.853282i
\(891\) 9.14643 + 23.7559i 0.306417 + 0.795853i
\(892\) 13.0000 + 22.5167i 0.435272 + 0.753914i
\(893\) 0 0
\(894\) −3.11416 33.7980i −0.104153 1.13037i
\(895\) 4.00000 4.89898i 0.133705 0.163755i
\(896\) 0 0
\(897\) 13.8564 + 19.5959i 0.462652 + 0.654289i
\(898\) 8.48528 + 4.89898i 0.283158 + 0.163481i
\(899\) −27.7128 48.0000i −0.924274 1.60089i
\(900\) 5.63505 + 13.9013i 0.187835 + 0.463377i
\(901\) 0 0
\(902\) 16.9706i 0.565058i
\(903\) 0 0
\(904\) 12.0000 0.399114
\(905\) 0 0
\(906\) 10.0424 21.7980i 0.333635 0.724189i
\(907\) 21.2132 12.2474i 0.704373 0.406670i −0.104601 0.994514i \(-0.533357\pi\)
0.808974 + 0.587844i \(0.200023\pi\)
\(908\) 2.44949 + 1.41421i 0.0812892 + 0.0469323i
\(909\) 17.3205 48.9898i 0.574485 1.62489i
\(910\) 0 0
\(911\) 48.0833i 1.59307i −0.604593 0.796535i \(-0.706664\pi\)
0.604593 0.796535i \(-0.293336\pi\)
\(912\) 0 0
\(913\) −4.00000 6.92820i −0.132381 0.229290i
\(914\) −29.3939 + 16.9706i −0.972263 + 0.561336i
\(915\) 21.2018 31.4719i 0.700911 1.04043i
\(916\) 19.5959i 0.647467i
\(917\) 0 0
\(918\) 6.92820 + 24.4949i 0.228665 + 0.808452i
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 2.15232 13.2426i 0.0709598 0.436597i
\(921\) 7.24745 15.7313i 0.238812 0.518365i
\(922\) −3.00000 + 5.19615i −0.0987997 + 0.171126i
\(923\) 11.3137i 0.372395i
\(924\) 0 0
\(925\) 0 0
\(926\) −7.34847 4.24264i −0.241486 0.139422i
\(927\) 29.4949 5.48188i 0.968740 0.180049i
\(928\) 25.4558 14.6969i 0.835629 0.482451i
\(929\) −22.5167 + 39.0000i −0.738748 + 1.27955i 0.214312 + 0.976765i \(0.431249\pi\)
−0.953059 + 0.302783i \(0.902084\pi\)
\(930\) 65.5692 + 4.54725i 2.15010 + 0.149110i
\(931\) 0 0
\(932\) 20.7846 0.680823
\(933\) −47.7975 + 4.40408i −1.56482 + 0.144183i
\(934\) −4.24264 + 2.44949i −0.138823 + 0.0801498i
\(935\) −2.86976 + 17.6569i −0.0938510 + 0.577441i
\(936\) 13.5065 + 15.7980i 0.441472 + 0.516372i
\(937\) −8.00000 −0.261349 −0.130674 0.991425i \(-0.541714\pi\)
−0.130674 + 0.991425i \(0.541714\pi\)
\(938\) 0 0
\(939\) 16.0000 + 22.6274i 0.522140 + 0.738418i
\(940\) −2.24264 5.91359i −0.0731469 0.192880i
\(941\) 12.1244 + 21.0000i 0.395243 + 0.684580i 0.993132 0.116998i \(-0.0373272\pi\)
−0.597889 + 0.801579i \(0.703994\pi\)
\(942\) 5.02118 10.8990i 0.163599 0.355108i
\(943\) 6.00000 10.3923i 0.195387 0.338420i
\(944\) −34.6410 −1.12747
\(945\) 0 0
\(946\) 24.0000 0.780307
\(947\) 1.73205 3.00000i 0.0562841 0.0974869i −0.836511 0.547951i \(-0.815408\pi\)
0.892795 + 0.450464i \(0.148741\pi\)
\(948\) 5.79796 12.5851i 0.188309 0.408744i
\(949\) 16.0000 + 27.7128i 0.519382 + 0.899596i
\(950\) 0 0
\(951\) −13.8564 19.5959i −0.449325 0.635441i
\(952\) 0 0
\(953\) 20.7846 0.673280 0.336640 0.941634i \(-0.390710\pi\)
0.336640 + 0.941634i \(0.390710\pi\)
\(954\) 0 0
\(955\) −43.6985 7.10228i −1.41405 0.229824i
\(956\) 2.44949 1.41421i 0.0792222 0.0457389i
\(957\) −27.5959 + 2.54270i −0.892049 + 0.0821938i
\(958\) −48.0000 −1.55081
\(959\) 0 0
\(960\) 0.267949 3.86370i 0.00864802 0.124700i
\(961\) 32.5000 56.2917i 1.04839 1.81586i
\(962\) 0 0
\(963\) −30.6520 + 5.69694i −0.987747 + 0.183581i
\(964\) 8.48528 + 4.89898i 0.273293 + 0.157786i
\(965\) −13.8564 + 16.9706i −0.446054 + 0.546302i
\(966\) 0 0
\(967\) 34.2929i 1.10278i 0.834246 + 0.551392i \(0.185903\pi\)
−0.834246 + 0.551392i \(0.814097\pi\)
\(968\) 2.59808 4.50000i 0.0835053 0.144635i
\(969\) 0 0
\(970\) 4.97056 30.5826i 0.159595 0.981947i
\(971\) 10.3923 18.0000i 0.333505 0.577647i −0.649692 0.760198i \(-0.725102\pi\)
0.983196 + 0.182550i \(0.0584353\pi\)
\(972\) 1.00000 15.5563i 0.0320750 0.498970i
\(973\) 0 0
\(974\) 25.4558i 0.815658i
\(975\) −10.0131 33.1623i −0.320677 1.06204i
\(976\) 42.4264 24.4949i 1.35804 0.784063i
\(977\) 24.2487 + 42.0000i 0.775785 + 1.34370i 0.934352 + 0.356351i \(0.115979\pi\)
−0.158567 + 0.987348i \(0.550687\pi\)
\(978\) −4.04541 43.9048i −0.129358 1.40392i
\(979\) 29.3939i 0.939432i
\(980\) 0 0
\(981\) 10.0000 28.2843i 0.319275 0.903047i
\(982\) 21.2132 + 12.2474i 0.676941 + 0.390832i
\(983\) −2.44949 + 1.41421i −0.0781266 + 0.0451064i −0.538554 0.842591i \(-0.681029\pi\)
0.460428 + 0.887697i \(0.347696\pi\)
\(984\) 4.34847 9.43879i 0.138624 0.300898i
\(985\) 0 0
\(986\) −27.7128 −0.882556
\(987\) 0 0
\(988\) 0 0
\(989\) 14.6969 + 8.48528i 0.467335 + 0.269816i
\(990\) 15.7831 28.8252i 0.501621 0.916125i
\(991\) −4.00000 6.92820i −0.127064 0.220082i 0.795474 0.605988i \(-0.207222\pi\)
−0.922538 + 0.385906i \(0.873889\pi\)
\(992\) 44.0908 + 25.4558i 1.39988 + 0.808224i
\(993\) −28.0000 39.5980i −0.888553 1.25660i
\(994\) 0 0
\(995\) 0 0
\(996\) 0.449490 + 4.87832i 0.0142426 + 0.154575i
\(997\) −26.0000 45.0333i −0.823428 1.42622i −0.903115 0.429400i \(-0.858725\pi\)
0.0796863 0.996820i \(-0.474608\pi\)
\(998\) 3.46410 + 6.00000i 0.109654 + 0.189927i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 735.2.p.a.509.2 8
3.2 odd 2 inner 735.2.p.a.509.3 8
5.4 even 2 735.2.p.c.509.3 8
7.2 even 3 105.2.g.c.104.4 yes 4
7.3 odd 6 735.2.p.c.374.2 8
7.4 even 3 inner 735.2.p.a.374.1 8
7.5 odd 6 105.2.g.a.104.3 yes 4
7.6 odd 2 735.2.p.c.509.1 8
15.14 odd 2 735.2.p.c.509.2 8
21.2 odd 6 105.2.g.c.104.1 yes 4
21.5 even 6 105.2.g.a.104.2 yes 4
21.11 odd 6 inner 735.2.p.a.374.4 8
21.17 even 6 735.2.p.c.374.3 8
21.20 even 2 735.2.p.c.509.4 8
28.19 even 6 1680.2.k.c.209.4 4
28.23 odd 6 1680.2.k.a.209.1 4
35.2 odd 12 525.2.b.j.251.7 8
35.4 even 6 735.2.p.c.374.4 8
35.9 even 6 105.2.g.a.104.1 4
35.12 even 12 525.2.b.j.251.6 8
35.19 odd 6 105.2.g.c.104.2 yes 4
35.23 odd 12 525.2.b.j.251.2 8
35.24 odd 6 inner 735.2.p.a.374.3 8
35.33 even 12 525.2.b.j.251.3 8
35.34 odd 2 inner 735.2.p.a.509.4 8
84.23 even 6 1680.2.k.a.209.4 4
84.47 odd 6 1680.2.k.c.209.1 4
105.2 even 12 525.2.b.j.251.1 8
105.23 even 12 525.2.b.j.251.8 8
105.44 odd 6 105.2.g.a.104.4 yes 4
105.47 odd 12 525.2.b.j.251.4 8
105.59 even 6 inner 735.2.p.a.374.2 8
105.68 odd 12 525.2.b.j.251.5 8
105.74 odd 6 735.2.p.c.374.1 8
105.89 even 6 105.2.g.c.104.3 yes 4
105.104 even 2 inner 735.2.p.a.509.1 8
140.19 even 6 1680.2.k.a.209.2 4
140.79 odd 6 1680.2.k.c.209.3 4
420.299 odd 6 1680.2.k.a.209.3 4
420.359 even 6 1680.2.k.c.209.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.g.a.104.1 4 35.9 even 6
105.2.g.a.104.2 yes 4 21.5 even 6
105.2.g.a.104.3 yes 4 7.5 odd 6
105.2.g.a.104.4 yes 4 105.44 odd 6
105.2.g.c.104.1 yes 4 21.2 odd 6
105.2.g.c.104.2 yes 4 35.19 odd 6
105.2.g.c.104.3 yes 4 105.89 even 6
105.2.g.c.104.4 yes 4 7.2 even 3
525.2.b.j.251.1 8 105.2 even 12
525.2.b.j.251.2 8 35.23 odd 12
525.2.b.j.251.3 8 35.33 even 12
525.2.b.j.251.4 8 105.47 odd 12
525.2.b.j.251.5 8 105.68 odd 12
525.2.b.j.251.6 8 35.12 even 12
525.2.b.j.251.7 8 35.2 odd 12
525.2.b.j.251.8 8 105.23 even 12
735.2.p.a.374.1 8 7.4 even 3 inner
735.2.p.a.374.2 8 105.59 even 6 inner
735.2.p.a.374.3 8 35.24 odd 6 inner
735.2.p.a.374.4 8 21.11 odd 6 inner
735.2.p.a.509.1 8 105.104 even 2 inner
735.2.p.a.509.2 8 1.1 even 1 trivial
735.2.p.a.509.3 8 3.2 odd 2 inner
735.2.p.a.509.4 8 35.34 odd 2 inner
735.2.p.c.374.1 8 105.74 odd 6
735.2.p.c.374.2 8 7.3 odd 6
735.2.p.c.374.3 8 21.17 even 6
735.2.p.c.374.4 8 35.4 even 6
735.2.p.c.509.1 8 7.6 odd 2
735.2.p.c.509.2 8 15.14 odd 2
735.2.p.c.509.3 8 5.4 even 2
735.2.p.c.509.4 8 21.20 even 2
1680.2.k.a.209.1 4 28.23 odd 6
1680.2.k.a.209.2 4 140.19 even 6
1680.2.k.a.209.3 4 420.299 odd 6
1680.2.k.a.209.4 4 84.23 even 6
1680.2.k.c.209.1 4 84.47 odd 6
1680.2.k.c.209.2 4 420.359 even 6
1680.2.k.c.209.3 4 140.79 odd 6
1680.2.k.c.209.4 4 28.19 even 6